Mathematics

You're working with a secant value in the third quadrant, where both sine and cosine are negative. The key is to use the reciprocal relationship $\cos\beta = \frac{1}{\sec\beta}$ to find $\cos\beta$, then the Pythagorean identity to find $\sin\beta$. Once you have both, the expression breaks into two manageable pieces: a product $\sin\beta\cos\beta$ and a ratio squared $\tan^2\beta = \frac{\sin^2\beta}{\cos^2\beta}$.

You're working with a secant value in the third quadrant, where both sine and cosine are negative. The key is to use the reciprocal relationship $\cos\beta = \frac{1}{\sec\beta}$ to find $\cos\beta$, then the Pythagorean identity to find $\sin\beta$. Once you have both, the expression breaks into two manageable pieces: a product $\sin\beta\cos\beta$ and a ratio squared $\tan^2\beta = \frac{\sin^2\beta}{\cos^2\beta}$.